初值间断的Navier-Stokes方程柯西问题弱解的存在性  

Cauchy Problem for One-dimensional Barotropic Compressible Navier-Stokes Equations with Density-dependent Viscosity and Discontinuous Initial Data

作　　者：王军礼[1,2] 毕佳成 连汝续[4] 马悦[4] 

机构地区：[1]北京大学光华管理学院,北京100871 [2]首都师范大学数学科学学院,北京100048 [3]西安电子科技大学计算机学院,西安710071 [4]华北水利水电大学数学与信息科学学院,郑州450045

出　　处：《河南师范大学学报（自然科学版）》2016年第1期8-14,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：河南省自然科学基金(14B110037)

摘　　要：主要研究了初值间断的一维可压缩Navier-Stokes方程的柯西问题.当初始密度间断任意大时,证明了黏性系数依赖密度的一维可压缩Navier-Stokes方程柯西问题整体弱解的存在性、分段正则性.并证明了密度的跳跃间断以指数速率衰减到零,同时弱解也趋于平衡态等.This paper is concerned with the Cauchy problem for one-dimensional barotropic compressible Navier-Stokesequations with density-dependent viscosity coefficient and discontinuous initial data. For the Cauchy problem,we prove that there exists a unique global pieeewise regular solution for piecewise regular initial density with arbitrarily large jump discontinu- ity. Moreover, we show that the jump of density decays exponentially in time and the piecewise regular solution also decays as time tends to infinity.

关 键 词：NAVIER-STOKES方程 柯西问题 初值间断 弱解 

分 类 号：O29[理学—应用数学]